Research on the fitting effects of several classical phenomenological hyperelastic constitutive models: considering the bulk modulus of rubber materials

To improve stress–strain prediction accuracy for dense vulcanized rubber, this study develops a constitutive modeling fitting framework incorporating bulk modulus (K) effects (i.e., a nearly incompressible formulation). Six classical phenomenological hyperelastic models—Three-Term Mooney-Rivlin (MR_T), Yeoh, Yeoh_Revised (Yeoh_R), Gent-Gent (GGent), Ogden, and Lopez-Pamies—are comparatively evaluated within this framework. Systematic assessment via the goodness-of-fit (R²) metric quantifies model performance across three deformation modes (simple tension, planar tension, and equibiaxial tension) for multiple rubber materials, including HNBR, FPM, silicone rubber, and the Treloar dataset. The framework is further extended to highly compressible rubber-like materials (e.g., foams/hydrogels). Key results demonstrate: (i) Significant R² improvement for comprehensive tensile stress predictions in dense vulcanized rubber; (ii) Pronounced enhancement of equibiaxial tensile stress accuracy for generalized Mooney-Rivlin models (e.g., MR_T, Yeoh_R); (iii) Critical dependence of the Ogden model on parameter initialization to ensure physical relevance and mitigate sensitivity; (iv) Limited applicability to highly compressible materials with strong model-specific performance variation; (v) Essential requirement for comprehensive experimental validation, particularly high-precision bulk modulus (K) characterization. This work provides quantitative selection criteria for phenomenological constitutive models in FEA, incorporating the calculation of shear modulus (G) to enable more reliable assessment of rubber material behavior in engineering applications.